I don't know if this will work but have you tried showing that any two 4-regular graph on 6 vertices are isomorphic?
That will be a graph obtained by removing 3 edges from complete graph on 5 vertices .
proof .
consider 5-regular graph with 6 vertices it is nothing but complete graph on 5 vertices .Now you need to reduce one degree for each of six vertices that is you need to remove 3 edges.
That will be a graph obtained by removing 3 edges from complete graph on 5 vertices .
proof .
consider 5-regular graph with 6 vertices it is nothing but complete graph on 5 vertices .Now you need to reduce one degree for each of six vertices that is you need to remove 3 edges.